Penalised Euclidean distance regression
A method is introduced for variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The methodology involves minimising a penalised Euclidean distance, where the penalty is the geometric mean of the $\ell_1$ an...
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| Format: | Article |
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Wiley
2018
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| Online Access: | https://eprints.nottingham.ac.uk/48710/ |
| _version_ | 1848797829794889728 |
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| author | Vasiliu, Daniel Dey, Tanujit Dryden, Ian L. |
| author_facet | Vasiliu, Daniel Dey, Tanujit Dryden, Ian L. |
| author_sort | Vasiliu, Daniel |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A method is introduced for variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The methodology involves minimising a penalised Euclidean distance, where the penalty is the geometric mean of the $\ell_1$ and $\ell_2$ norms of the regression coefficients. This particular formulation exhibits a grouping effect, which is useful for model selection in high dimensional problems. Also, an important result is a model consistency theorem, which does not require an estimate of the noise standard deviation. An algorithm for estimation is described, which involves thresholding to obtain a sparse solution. Practical performances of variable selection and prediction are evaluated through simulation studies and the analysis of real datasets. |
| first_indexed | 2025-11-14T20:10:06Z |
| format | Article |
| id | nottingham-48710 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:10:06Z |
| publishDate | 2018 |
| publisher | Wiley |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-487102020-05-04T19:27:55Z https://eprints.nottingham.ac.uk/48710/ Penalised Euclidean distance regression Vasiliu, Daniel Dey, Tanujit Dryden, Ian L. A method is introduced for variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The methodology involves minimising a penalised Euclidean distance, where the penalty is the geometric mean of the $\ell_1$ and $\ell_2$ norms of the regression coefficients. This particular formulation exhibits a grouping effect, which is useful for model selection in high dimensional problems. Also, an important result is a model consistency theorem, which does not require an estimate of the noise standard deviation. An algorithm for estimation is described, which involves thresholding to obtain a sparse solution. Practical performances of variable selection and prediction are evaluated through simulation studies and the analysis of real datasets. Wiley 2018-01-22 Article PeerReviewed Vasiliu, Daniel, Dey, Tanujit and Dryden, Ian L. (2018) Penalised Euclidean distance regression. Stat, 7 (1). e175/1-e175/14. ISSN 2049-1573 Euclidean distance; grouping; penalization; prediction; regularization; sparsity; variable screening http://onlinelibrary.wiley.com/doi/10.1002/sta4.175/abstract doi:10.1002/sta4.175 doi:10.1002/sta4.175 |
| spellingShingle | Euclidean distance; grouping; penalization; prediction; regularization; sparsity; variable screening Vasiliu, Daniel Dey, Tanujit Dryden, Ian L. Penalised Euclidean distance regression |
| title | Penalised Euclidean distance regression |
| title_full | Penalised Euclidean distance regression |
| title_fullStr | Penalised Euclidean distance regression |
| title_full_unstemmed | Penalised Euclidean distance regression |
| title_short | Penalised Euclidean distance regression |
| title_sort | penalised euclidean distance regression |
| topic | Euclidean distance; grouping; penalization; prediction; regularization; sparsity; variable screening |
| url | https://eprints.nottingham.ac.uk/48710/ https://eprints.nottingham.ac.uk/48710/ https://eprints.nottingham.ac.uk/48710/ |